Faster than light travel and destination's time

I've read that faster than light travel is possible if we manipulate the space around the craft, but the energy needed is on the order of the sun's output.

So, even if not practical, since theoretically it is possible I want to ask what happens to our destination's time. As I understand at 0.99999 the speed of light, we will arrive at a planet one light-year away in a mere seconds, but the planet will be one year older than when we started the journey.
What happens for the same distance scenario for speeds equal to light's and speeds greater than light's?

Alcubierre drive. Also energy estimates I've read go millions of times the industrial energy production to sun's output. Both cases impractical today. But the point is that the AD does not contradict relativity.

"We have shown that there exist very physical configurations of an ideal fluid which give rise to solutions of the Einstein equations that correspond asymptotically to negative mass Schwarzschild-de Sitter space times. The energy-momentum tensor that gives rise to such space times is perfectly physical, it everywhere satisfies the dominant energy condition. Since the space time is not asymptotically flat, we evade the positive energy theorems which would not allow for negative mass. Negative mass configurations therefore can exist in de Sitter backgrounds, exactly as have been proposed for the inflationary phase of the early universe."

"We have shown that there exist very physical configurations of an ideal fluid which give rise to solutions of the Einstein equations that correspond asymptotically to negative mass Schwarzschild-de Sitter space times. The energy-momentum tensor that gives rise to such space times is perfectly physical, it everywhere satisfies the dominant energy condition. Since the space time is not asymptotically flat, we evade the positive energy theorems which would not allow for negative mass. Negative mass configurations therefore can exist in de Sitter backgrounds, exactly as have been proposed for the inflationary phase of the early universe."

Alcubierre's metric violates the dominant energy condition. The material you've quoted discusses spacetimes that satisfy the dominant energy condition, and therefore isn't relevant. In any case, this seems to have little to do with your initial question.

So, even if not practical, since theoretically it is possible I want to ask what happens to our destination's time. As I understand at 0.99999 the speed of light, we will arrive at a planet one light-year away in a mere seconds, but the planet will be one year older than when we started the journey.

What happens for the same distance scenario for speeds equal to light's and speeds greater than light's?

If you have an Alcuibierre drive, it's automatically also a time machine -- in technical language, you can use it to create closed, timelike curves (CTCs). That means that you could, for example, fly to another star, find out that the aliens there are hostile, return, get back before you left, and warn yourself not to take the trip in the first place.

If you have an Alcuibierre drive, it's automatically also a time machine -- in technical language, you can use it to create closed, timelike curves (CTCs). That means that you could, for example, fly to another star, find out that the aliens there are hostile, return, get back before you left, and warn yourself not to take the trip in the first place.

Supposed we can travel 4 times the speed of light.
So A can reach C in 1 year (distance is 4 ly).
And go back to Blue wl in 1 year later.
But there's no way that A can go back to F, right?
How can Blue from event A can warn him/herself if Blue at event A can't go back to F?
##\tau = \sqrt{1^2-4^2}##Now, this equation is a problem ##\tau = \sqrt{15}i##?

View attachment 86679
Supposed we can travel 4 times the speed of light.
So A can reach C in 1 year (distance is 4 ly).
And go back to Blue wl in 1 year later.
But there's no way that A can go back to F, right?
How can Blue from event A can warn him/herself if Blue at event A can't go back to F?
##\tau = \sqrt{1^2-4^2}##Now, this equation is a problem ##\tau = \sqrt{15}i##?

That is correct.

In SR faster than light travel is not defined so the calculation for ##\tau## will not give a sensible answer.

(##\sqrt{1^2-4^2}=\sqrt{-15}## ?? )

CTCs allow you to travel in time without FTL speeds. They require curved spacetime. The Godel spacetime is a strange beast though, nothing like our own universe.

But Hawking said "It turns out that a mathematical model involving imaginary time predicts not only effects we have already observed but also effects we have not been able to measure yet nevertheless believe in for other reasons."

Myself I don't believe in time machines, since I have never seen glass debri rise from the floor and assembe a glass on the table, but I play devil's advocate whenever I can. So is imaginary time only a mathematical concept?

Staff: Mentor

But Hawking said "It turns out that a mathematical model involving imaginary time predicts not only effects we have already observed but also effects we have not been able to measure yet nevertheless believe in for other reasons."

Myself I don't believe in time machines, since I have never seen glass debri rise from the floor and assembe a glass on the table, but I play devil's advocate whenever I can. So is imaginary time only a mathematical concept?

The imaginary time that Hawking is talking about is a completely separate concept from the imaginary time Mentz114 is talking about. Hawking us talking about using a Euclidean metric with an imaginary coordinate time. Mentz114 is talking about using a Lorentzian metric with a spacelike proper time.

Many people here also do not believe in time machines, which is why they think that any exotic matter solution to the EFE is non physical (including the Alcuibere drive)

View attachment 86679
Supposed we can travel 4 times the speed of light.
So A can reach C in 1 year (distance is 4 ly).
And go back to Blue wl in 1 year later.
But there's no way that A can go back to F, right?
How can Blue from event A can warn him/herself if Blue at event A can't go back to F?
##\tau = \sqrt{1^2-4^2}##Now, this equation is a problem ##\tau = \sqrt{15}i##?

Your diagram and your reasoning are based on special relativity. SR doesn't have CTCs.

Staff: Mentor

SR would still allow to get back in time, if FTL is possible in some frame and if all frames have the same laws of physics.
The C->F track is 4 times the speed of light in some other reference frame, and we assumed that moving at 4 times the speed of light is possible (in every frame).

SR would still allow to get back in time, if FTL is possible in some frame and if all frames have the same laws of physics.
The C->F track is 4 times the speed of light in some other reference frame, and we assumed that moving at 4 times the speed of light is possible (in every frame).

This is unrelated to the Alcubierre metric and the CTCs that it makes possible. Also, it doesn't make much sense to say what SR would predict if SR allowed "moving at 4 times the speed of light," by which I assume you mean the motion of a material object such as a person or a spaceship. SR doesn't allow that. We can't say what SR would predict in a situation that SR says is impossible.

Staff: Mentor

This is unrelated to the Alcubierre metric and the CTCs that it makes possible.

Right, it is much more general.
There is nothing in SR that fundamentally rules out FTL, if you give up causality (which is exactly the point here) and if you are happy with questionable mass/energy relations. The equations work for superluminal things as well.

There is nothing in SR that fundamentally rules out FTL, if you give up causality (which is exactly the point here) and if you are happy with questionable mass/energy relations. The equations work for superluminal things as well.